Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I would like to find a fixed point of f^4 in tems of a and b. I define function as

 

I calculate f(f(f(f(x,y))))  and Iet f(f(f(f(x,y)))) = (x,y), then use the solve command as:

solve({b^4*(a*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)^2-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*b^2*(a*x-x^2-x*y)*x*y)*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*(a*x-x^2-x*y)*x*y = y, a*(a*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)^2-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*b^2*(a*x-x^2-x*y)*x*y)-(a*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)^2-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*b^2*(a*x-x^2-x*y)*x*y)^2-(a*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)^2-(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*b^2*(a*x-x^2-x*y)*x*y)*b^3*(a*(a*x-x^2-x*y)-(a*x-x^2-x*y)^2-(a*x-x^2-x*y)*b*x*y)*(a*x-x^2-x*y)*x*y = x}, {x, y})

My computer was freezing. How can I get my result. Thank you

 

How would I solve a linear algebra differential equation with initial conditions.

 

For example, what if I had:

 

x'(t) = [1 2 ; 3 4] x(t) such that the ics: (0,1)

 

I try to write a Maple Code. But I can' t finish it. 

This is very important for me. Could you help me? download_Maple Code.mw

I am using foslve to get the numerical solution of a very complex equition. When I rerun the code with different Digits settings, I got different solutions. I guess it is not surpprising since it is a numerical solution, but how can I trust/choose which one to use?? Is there anyway to unify the solutions regardless the Digits settings.

This attached are when Digits:=30 and Digits:=20 respectively.. Note, the K is a very large nubmer.. the X is a beta distribution..

Hi guys, 

I have tried to create a loop to solve a set of two equations, but can't seem to get it working. My initial equations are given by;

 

nstar := (F, L, sigma) -> ceil((ln(k*F) - ln(c(L, sigma)*B))/ln(Phi(L, sigma)))

 

and 

 

i := (F, L, sigma) -> r*(1 - (G(L, sigma)*Phi(L, sigma))^nstar(F, L, sigma)*B/F)/(1 - G(L, sigma)^nstar(F, L, sigma))

 

in which both are based on further rather simple equations. To these I am trying to apply the proc function where I am trying to find which i makes borth the equations above work :

 

i := proc(F,L,sigma)  

local k :=0.01 ;  

local eps := 0.01 ;  

do while(eps>0.001)  

nstar:= (6)

i := (7)

eps:= i -k:

k=i:

end do;

k;

end proc;


Error, Got internal error in Typesetting:-Parse : "'_Inert_DELAYLESSTHAN' is not a valid inert form"
 

But as you see I am here getting a error which I have not managed to fix. Can anyone see where I might have gone wrong? Could this be done by solve or fsolve? If yes, then how (have tried it as well without succeding)?

We have just released updates to Maple and MapleSim.

Maple 2019.2 includes corrections and improvements to a variety of areas in the product, including a new “Go to page ____” option in print preview (that am personally quite pleased about), sections are expanded by default when printing or exporting, a fix to a problem using non-executable math with text in document mode that sometimes made it impossible to advance to a new line using Enter, improvements to VectorCalculus, select, abs and other math functions, support for macOS Catalina, and more.  We recommend that all Maple 2019 users install these updates.

This update is available through Tools>Check for Updates in Maple, and is also available from our website on the Maple 2019.2 download page, where you can also find more details.

For MapleSim users, the MapleSim 2019.2 family of products includes enhancements in the areas of model development and toolchain connectivity, including substantial enhancements to the MapleSim CAD toolbox.   For more details and download instructions, visit the MapleSim 2019.2 download page.

help me! 

 

I have a problem with the system, looking forward to everyone's help!

expand((x-c)^2+(y-d)^2-R^2) = 0; algsubs(-R^2+c^2+d^2 = f, %); P := proc (x, y) options operator, arrow; -2*x*c-2*y*d+x^2+y^2+f = 0 end proc; 2 2 P := (x, y) -> -2 x c - 2 y d + x + y + f = 0 P(a*cos(theta), b*sin(theta)); G := unapply(%, theta); #usage des formules d'Euler simplify(expand(4*(exp(I*theta))^2*subs(cos(theta) = (exp(I*theta)+exp(-I*theta))*(1/2), sin(theta) = (exp(I*theta)-exp(-I*theta))/(2*I), G(theta)))); poly := sort(subs(exp(I*theta) = X, exp((2*I)*theta) = X^2, exp((3*I)*theta) = X^3, exp((4*I)*theta) = X^4, %)); coeff(lhs(poly), X^4)/tcoeff(lhs(poly)); # exp(I*theta1),exp(I*theta2),exp(I*theta3),exp(I*theta4) sont les racines de ce polynôme unitaire : exp(I*theta1)*exp(I*theta2)*exp(I*theta3)*exp(I*theta4) =1 exp(I*(θ1+θ2+θ3+θ4)=1 d'où θ1+θ2+θ3+θ4 ≡ 2*Pi

I am trying to construct a procedure which makes a boxplot from a list using the statistics package. 

I have come to this here. However it shows both the x and y - axis. Is there any way to make it show a horizontal boxplot like in my code. But only displays the x- axis ? Meaning the values from the plot? Plus any to make it not stick to x-axis like my code does? I tried the command scale, but it doesn't work in statistics package 

    BoxP:=proc(xd::list) 
        uses Statistics:
        return plots[display](BoxPlot(xd,deciles = false,orientation=horizontal),size=[600,400],axes=normal);
    end proc;

Greetings, 

Any maple user have any idea how to solve coupled difference scheme system of equations using crank nicolson scheme 

Assume 

matrix([[1,0],[0,1]]) * matrix[[y],[y']]
= a system 

 

how to get back matrix([[1,0],[0,1]]) from this system in general method if the system is very large?

Is there a function to convert recurrence equation to a system of equations?

 

I think we will write nested for loops or nested sequences. But I can' t achieve.

Could you help me?

EDITED AND EXTENDED:

In fact, the original question is as follows:

and

where it is a standard inner product on L^2 and u(x,t) is a function. For example; u(x,t) =x*t etc.

(The screenshots is taken from a book)

I want to write a code for finding Matrix U whose elements are u_ij.

Hello!

How can I make MAPLE to create the solution of the following system?

Program of Transfer matrix method for solving the vibrational behavior of a cracked beam. For more details and comprehension check the paper entitled ''A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions ''
 

restart; with(LinearAlgebra)NULLNULL

W11 := A[1]*cos(nu*x)+A[2]*sin(nu*x)+A[3]*cosh(nu*x)+A[4]*sinh(nu*x);

theta11 := -A[1]*nu*sin(nu*x)+A[2]*nu*cos(nu*x)+A[3]*nu*sinh(nu*x)+A[4]*nu*cosh(nu*x)  NULL

M11 := EI*(-A[1]*nu^2*cos(nu*x)-A[2]*nu^2*sin(nu*x)+A[3]*nu^2*cosh(nu*x)+A[4]*nu^2*sinh(nu*x))
S11 := EI*(A[1]*nu^3*sin(nu*x)-A[2]*nu^3*cos(nu*x)+A[3]*nu^3*sinh(nu*x)+A[4]*nu^3*cosh(nu*x))
 

MD11 := subs(A[1] = 1, A[2] = 0, A[3] = 0, A[4] = 0, W11); MD12 := subs(A[1] = 0, A[2] = 1, A[3] = 0, A[4] = 0, W11); MD13 := subs(A[1] = 0, A[2] = 0, A[3] = 1, A[4] = 0, W11); MD14 := subs(A[1] = 0, A[2] = 0, A[3] = 0, A[4] = 1, W11)
NULL

MD21 := subs(A[1] = 1, A[2] = 0, A[3] = 0, A[4] = 0, theta11); MD22 := subs(A[1] = 0, A[2] = 1, A[3] = 0, A[4] = 0, theta11); MD23 := subs(A[1] = 0, A[2] = 0, A[3] = 1, A[4] = 0, theta11); MD24 := subs(A[1] = 0, A[2] = 0, A[3] = 0, A[4] = 1, theta11)
 

MD31 := subs(A[1] = 1, A[2] = 0, A[3] = 0, A[4] = 0, M11); MD32 := subs(A[1] = 0, A[2] = 1, A[3] = 0, A[4] = 0, M11); MD33 := subs(A[1] = 0, A[2] = 0, A[3] = 1, A[4] = 0, M11); MD34 := subs(A[1] = 0, A[2] = 0, A[3] = 0, A[4] = 1, M11)
 

MD41 := subs(A[1] = 1, A[2] = 0, A[3] = 0, A[4] = 0, S11); MD42 := subs(A[1] = 0, A[2] = 1, A[3] = 0, A[4] = 0, S11); MD43 := subs(A[1] = 0, A[2] = 0, A[3] = 1, A[4] = 0, S11); MD44 := subs(A[1] = 0, A[2] = 0, A[3] = 0, A[4] = 1, S11)
 

 

TM := Matrix(4, 4, [[MD11, MD12, MD13, MD14], [MD21, MD22, MD23, MD24], [MD31, MD32, MD33, MD34], [MD41, MD42, MD43, MD44]])

C := Matrix(4, 4, [[1, 0, 0, 0], [0, 1, c44, 0], [0, 0, 1, 0], [0, 0, 0, 1]])NULL

NULL    TM2 := subs(x = 0, TM); TM3 := subs(x = L, TM)

with(MTM)

TM4 := inv(TM)NULLNULL 

TM5 := inv(TM2)NULL

Y11 := MatrixMatrixMultiply(TM3, TM4)

    Y22 := MatrixMatrixMultiply(C, TM)   

Y33 := MatrixMatrixMultiply(Y11, Y22)

Y44 := MatrixMatrixMultiply(Y33, TM5)NULL

BB11 := Y44[3, 3]

BB12 := Y44[3, 4]

BB21 := Y44[4, 3]

BB22 := Y44[4, 4] 

BB := Matrix(2, 2, [[BB11, BB12], [BB21, BB22]]) 

NULL

R11 := det(BB) 

NULL

L := .18; L1 := 1; h := 0.5e-2; b := 0.2e-1; rho := 957.5; area = b.h; m := rho*h*b; EI := 0.2682e10*b*h^3mu := ((m.(omega^2))*L^4/EI)^(1/4); x := .5; c44 := .1; c11 := 0NULLNULL

plot(R11, omega = 1 .. 100)

 

 

 

``

NULL

NULL


 

Download transfer.mw

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